Research ArticleOpen accessPhrase in the titleFractional Calculus Theoretical Evolution for Radiation QuantitiesAmin Al-Okour, Sherin A. Sareireh, Abdullah Ajlouni, Abdul-Wali AjlouniProblem statement: Radiation dosimetry features depend on semi-empirical formulas that lack a strong mathematical framework. This is due to the fact that the microscopic radiation interaction with matter includes energy losses that have never been described properly in quantum mechanics, which deals with conserved energy systems. Approach: Using the recent theory of the quantization of nonconservative systems using fractional calculus. … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 2 Feb 2012 · 6,661 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleFractional Calculus for Certain Integral Operator Involving Logarithmic CoefficientsAabed Mohammed, Maslina Darus, Daniel BreazProblem statement: Some properties of certain integral operators on some subclasses were studied. Approach: Certain classes defined by integral operators were introduced. The well known definitions and preliminaries results were stated. Results: Having new integral operator, the characterization problems were discussed. Thus sufficient conditions were given. Conclusion: Therefore, by having new integral operators, sufficient conditions were determined. In fact, other … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Sep 2009 · 7,181 accessesView PDFCite
Research ArticleOpen accessIn the keywordsSufficient Conditions for Subordination of Meromorphic FunctionsRabha W. Ibrahim, Maslina DarusProblem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems … …Journal of Mathematics and Statistics, Vol. 5, Issue 3 · 30 Sep 2009 · 7,208 accessesView PDFCite
Research ArticleOpen accessIn the keywordsApproximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform MethodEman Abuteen, Asad Freihat, Mohammed Al-Smadi et al.This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different … …Journal of Mathematics and Statistics, Vol. 12, Issue 1 · 26 Mar 2016 · 7,901 accessesView PDFCite
Research ArticleOpen accessIn the abstractFractional Quantum Field Theory on Multifractals SetsEl-Nabulsi Ahmad RamiProblem statement: This study is a contribution to the general program of describing complex dynamical systems using the tool of fractional calculus of variations. Approach: Following our previous work, fractional quantum field theory based on the fractional actionlike variational approach supported by Saxena-Kumbhat fractional integrals functionals, fractional derivative of order (α, β) and dynamical fractional exponent on multi-fractal sets is … …American Journal of Engineering and Applied Sciences, Vol. 4, Issue 1 · 15 Mar 2011 · 7,343 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn Certain Classes of Multivalent Analytic FunctionsRabha W. Ibrahim, Maslina DarusProblem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Livingston. Approach: A new class of multivalent … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 7,438 accessesView PDFCite
Research ArticleOpen accessIn the abstractSome Properties of Certain Subclass of Meromorphically Multivalent Functions Defined By Linear OperatorF. Ghanim, M. DarusProblem statement: By means of the Hadamard product (or convolution), a linear operator was introduced. This operator was motivated by many authors namely Srivastava, Swaminathan, Owa and many others. The operator was indeed needed to create new ideas in the area of geometric function theory. Approach: The linear operator of meromorphic p-valent functions was proposed and defined. The preliminary concept … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,342 accessesView PDFCite